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paper v0.13: the Green-persona approachability revision

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A referee persona (deep crypto, shallow Lean, no prior drafts) read the
whole paper; all findings applied, ~40 edits, none touching technical
content:
- house terms defined at first use: certificate (in contributions),
  accumulator (= the log's Merkle tree + verifiers), signed view (4.2),
  pin rule/pin-store (named at their definition, 4.3), axiom cone as the
  one canonical synonym, loop-fidelity glossed, facade tied to its entry
  point, scope block named in 3.1, oracles marked 'uninterpreted
  function symbols, not random oracles'
- operator 'verdict' renamed label everywhere (Verdict stays the
  consumer algorithm); fork disambiguated (codebases vs fork evidence)
- notation: declarations T_i -> Theta_i (tier collision), HIST chain
  k kept but challenge scalar -> c and signature bytes -> R-bar
  (k/r_1 overloads resolved); tiers T1-T4 introduced in 6.1 body
- theorem-statement sensitivity: Thm 8 scoped to the recursive
  verifiers in the STATEMENT; Prop 1's 'exhibited' made conditional
  with pointer; Thm 3 carries its honest-pin note; Def 2(iii) gets the
  forgery caveat; Lemma 5 declared a restatement of Prop 2
- ghost references resolved (whole-tree root binding stated in place,
  twice); revision residue purged (Post-submission -> Subsequently
  closed; tense unified; hardened state, guarded replay, KNOWN-GAPS
  explained); 6.2 retitled 'A second instantiation'
- six triple-read sentences rewritten per referee (them-sentence,
  vacuous->trivially-by-counting with real non-vacuity guard wording,
  pin supplier, physical-execution antecedent, bridges-land, App E
  factorization)
- appendices A-D now each cited from the body; App D states its shared
  opaque boundary; FIPS 205 added to the bibliography [23] and cited
- abstract divergence sentence rewritten (divergence not 'boundary',
  past tense, closure named, 'the corresponding log entry')
Gate green: v0.13, 25pp; pages 1/16/25 eye-checked; suite 156.
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paper/README.md
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@ -1,13 +1,16 @@
# Which file is current? # Which file is current?
**`ltl.pdf` / `ltl.tex` — the current paper (v0.12, revised August 2026).** **`ltl.pdf` / `ltl.tex` — the current paper (v0.13, revised August 2026).**
The review process concluded in August 2026. v0.10 folded in the The review process concluded in August 2026. v0.10 folded in the
corrections queued during the freeze (the closed consistency-verifier corrections queued during the freeze (the closed consistency-verifier
divergence with its `sn = 0` root cause, replay-harness-integrity divergence with its `sn = 0` root cause, replay-harness-integrity
limitation, claim-matrix row); v0.11 brought the paper up to the live limitation, claim-matrix row); v0.11 brought the paper up to the live
system: the nineteen-leaf dual-signed deployment, the SLH-DSA (FIPS 205) system: the nineteen-leaf dual-signed deployment, the SLH-DSA (FIPS 205)
verify-path instantiation, and its certificate appendix; v0.12 unifies verify-path instantiation, and its certificate appendix; v0.12 unified
entry numbering on 0-based leaf indices throughout. The entry numbering on 0-based leaf indices; v0.13 is the approachability
revision from an external-persona referee pass (house terms defined at
first use, theorem statements carry their own scoping, notation
collisions resolved, FIPS 205 reference added). The
version submitted for review (July 17, 2026, sha256 `7f140356…`) is version submitted for review (July 17, 2026, sha256 `7f140356…`) is
preserved unchanged in this repository's git history. The live copy at preserved unchanged in this repository's git history. The live copy at
<https://ltl.zkdefi.org/paper> serves the current revision. <https://ltl.zkdefi.org/paper> serves the current revision.

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@ -48,7 +48,7 @@ showstringspaces=false,breaklines=true,xleftmargin=.5em,xrightmargin=.5em}
\large A Transparency Model and the Lean Transparency Log} \large A Transparency Model and the Lean Transparency Log}
\author{Olaf Horvath\\ \author{Olaf Horvath\\
\small Olaf.Horvath@zkdefi.org \quad ORCID 0009-0004-8008-5805} \small Olaf.Horvath@zkdefi.org \quad ORCID 0009-0004-8008-5805}
\date{July 2026 \\ {\normalsize Revised: August 2026 --- v0.12}} \date{July 2026 \\ {\normalsize Revised: August 2026 --- v0.13}}
\begin{document} \begin{document}
\maketitle \maketitle
@ -82,11 +82,12 @@ project-specific uninterpreted SHA-256 boundary axiom) and, as its newest
entry, eleven certificates over the SLH-DSA-SHA2-128s verifier. Since tree entry, eleven certificates over the SLH-DSA-SHA2-128s verifier. Since tree
size 14 every signed head additionally carries a deterministic SLH-DSA size 14 every signed head additionally carries a deterministic SLH-DSA
co-signature --- produced with the parameter set whose verification path the co-signature --- produced with the parameter set whose verification path the
log itself attests. The mechanization effort also exposed, log itself attests. The mechanization effort also exposed, via
via differential testing, a nontrivial implementation boundary --- the differential testing, a nontrivial model/implementation divergence --- on
deployed iterative consistency verifier is not extensionally equal to the malformed size claims, the deployed iterative consistency verifier was not
recursive model on malformed size claims --- and the leaf records this extensionally equal to the recursive model proved in Lean (since closed;
limitation explicitly. The contribution is a cryptographic distribution this paper reports the pre-closure measurements) --- recorded explicitly
in the corresponding log entry. The contribution is a cryptographic distribution
model for machine-checked correctness evidence, with an end-to-end deployed model for machine-checked correctness evidence, with an end-to-end deployed
instantiation that carries scoped proofs about its own accountability instantiation that carries scoped proofs about its own accountability
machinery. machinery.
@ -147,7 +148,9 @@ temporal logic~\cite{pnueli}; we note the collision once and rely on context.}
is the complete instantiation evaluated in this paper. Its subjects are four is the complete instantiation evaluated in this paper. Its subjects are four
Rust Ed25519 codebases with Lean~4~\cite{lean4} certificates against extracted Rust Ed25519 codebases with Lean~4~\cite{lean4} certificates against extracted
models. Leaf 12 --- its thirteenth entry --- attests the Lean corpus models. Leaf 12 --- its thirteenth entry --- attests the Lean corpus
that mechanizes the log's own accumulator arguments. Thus the paper's central that mechanizes the security arguments of the log's own Merkle accumulator
(the tree of \S\ref{sec:construction} together with its inclusion and
consistency verifiers). The paper's central
claim survives replacement of Lean, Ed25519, or RFC~9162 by other components; claim survives replacement of Lean, Ed25519, or RFC~9162 by other components;
what is essential is the distribution and accountability model. what is essential is the distribution and accountability model.
@ -169,8 +172,8 @@ those observations with their own policy; operator labels can veto but cannot
grant acceptance. We state clearly that axiom-name equality is not semantic grant acceptance. We state clearly that axiom-name equality is not semantic
identity of theorem statements. identity of theorem statements.
\item \textbf{A deployed cryptographic case study.} \item \textbf{A deployed cryptographic case study.}
The log contains nineteen leaves: three four-fork replay generations for the The log contains nineteen leaves: three replay generations across the four
Ed25519 codebases (the newest at 44 certificates per fork), two attestations Ed25519 codebases (the newest at 44 certificates per fork; a \emph{certificate} throughout this paper is one theorem's kernel-checked proof together with its recorded axiom cone), two attestations
of the accumulator's own Lean corpus (leaf 12 carries an environment-derived of the accumulator's own Lean corpus (leaf 12 carries an environment-derived
audit inventory of 222 compiled constants, 61 human-reviewed certificate audit inventory of 222 compiled constants, 61 human-reviewed certificate
cones, and a single uninterpreted SHA-256 axiom; leaf 17 re-attests the cones, and a single uninterpreted SHA-256 axiom; leaf 17 re-attests the
@ -183,7 +186,7 @@ verifier and the recursive model proved in Lean are not extensionally equal:
there are malformed size/root combinations accepted only by the deployed there are malformed size/root combinations accepted only by the deployed
verifier. We characterize 3,867 divergences in 73,573 pinned boundary tests verifier. We characterize 3,867 divergences in 73,573 pinned boundary tests
--- every one deployed-accepts-only --- and scope the public attestation --- every one deployed-accepts-only --- and scope the public attestation
accordingly. (Post-submission closure, July 2026: the divergence was traced to accordingly. (Subsequently closed: the divergence was traced to
the deployed verifier omitting RFC~9162 \S2.1.4.2 Step~7's terminal the deployed verifier omitting RFC~9162 \S2.1.4.2 Step~7's terminal
$sn=0$ condition; restoring that one conjunct removes every divergence in the $sn=0$ condition; restoring that one conjunct removes every divergence in the
pinned family, confirmed by a three-way regression against an independent pinned family, confirmed by a three-way regression against an independent
@ -197,16 +200,18 @@ binary correspondence, compiler correctness, extraction faithfulness,
side-channel resistance, SHA-512 correctness, or execution provenance of the side-channel resistance, SHA-512 correctness, or execution provenance of the
signing binary. The present leaf schema identifies theorem declarations by signing binary. The present leaf schema identifies theorem declarations by
repository commit and name, not by a canonical digest of their elaborated Lean repository commit and name, not by a canonical digest of their elaborated Lean
types. These are explicit boundaries, not hidden qualifications. types. These are explicit boundaries, not hidden qualifications
(Appendix~\ref{app:matrix} tabulates every consumer-facing claim with its
establishing mechanism and remaining assumption).
\section{The distribution problem}\label{sec:problem} \section{The distribution problem}\label{sec:problem}
\subsection{Three evidence modes} \subsection{Three evidence modes}
Let a subject repository at commit $g$ contain theorem declarations Let a subject repository at commit $g$ contain theorem declarations
$T_1,\dots,T_q$. A deterministic verifier execution produces an observation $\Theta_1,\dots,\Theta_q$. A deterministic verifier execution produces an observation
$O_g$ containing success/failure and the reported assumption cone of each $O_g$ containing success/failure and the reported \emph{axiom cone} (synonymously, the observed axiom-name set) of each
$T_i$ --- the set of axioms the checked proof of $T_i$ ultimately rests on. There are three natural ways to consume this result. $\Theta_i$ --- the set of axioms the checked proof of $\Theta_i$ ultimately rests on. There are three natural ways to consume this result.
\begin{description}[leftmargin=1.5em,itemsep=4pt] \begin{description}[leftmargin=1.5em,itemsep=4pt]
\item[Direct replay.] The consumer reconstructs the verifier environment and \item[Direct replay.] The consumer reconstructs the verifier environment and
@ -293,7 +298,8 @@ A replay attestation $a$ contains at least
\] \]
where $N_i$ is a declaration name, $s_i$ is replay status, and $A_i$ is the where $N_i$ is a declaration name, $s_i$ is replay status, and $A_i$ is the
observed axiom-name set. The deployed schema additionally carries diagnostics, observed axiom-name set. The deployed schema additionally carries diagnostics,
resource controls, scope, and exclusions. resource controls, a machine-readable \emph{scope block} (the deployed
leaf-12 instance is quoted verbatim in Appendix~\ref{app:entry13}), and exclusions.
\begin{definition}[Attestation-transparency scheme] \begin{definition}[Attestation-transparency scheme]
An attestation-transparency scheme is a~\mbox{tuple} An attestation-transparency scheme is a~\mbox{tuple}
@ -304,7 +310,7 @@ An attestation-transparency scheme is a~\mbox{tuple}
over a hash function and signature scheme. $\mathsf{Append}$ commits the over a hash function and signature scheme. $\mathsf{Append}$ commits the
canonical serialization of an attestation as the next leaf and returns a signed canonical serialization of an attestation as the next leaf and returns a signed
tree head. $\mathsf{Verdict}$ is parameterized by consumer-local policy and tree head. $\mathsf{Verdict}$ is parameterized by consumer-local policy and
does not consume an operator verdict as positive evidence. does not consume an operator label as positive evidence.
\end{definition} \end{definition}
\begin{definition}[Accountable replay distribution] \begin{definition}[Accountable replay distribution]
@ -315,9 +321,10 @@ determined leaf value at its claimed position; (ii) a
consumer accepts a later view only as the same view or a verified extension; consumer accepts a later view only as the same view or a verified extension;
(iii) two valid equal-size heads with unequal roots, in one log and protocol (iii) two valid equal-size heads with unequal roots, in one log and protocol
context, form transferable evidence context, form transferable evidence
that the key holder signed incompatible views; and (iv) positive acceptance of that the key holder signed incompatible views, except under signature
forgery; and (iv) positive acceptance of
a theorem boundary is a function of recorded observations and consumer-local a theorem boundary is a function of recorded observations and consumer-local
policy, not of an operator verdict. policy, not of an operator label.
\end{definition} \end{definition}
The definition is intentionally an accountability property, not a validity The definition is intentionally an accountability property, not a validity
@ -389,8 +396,8 @@ of the operator public key.
The model deliberately does not cryptographically exclude fabricated kernel The model deliberately does not cryptographically exclude fabricated kernel
observations; the same holds when the operator's replay harness is defective observations; the same holds when the operator's replay harness is defective
rather than dishonest. That is a statement about a physical execution on the operator's rather than dishonest. Whether the kernel actually ran as claimed is a
machine. The mechanism instead makes the claimed execution target precise fact about a physical execution on the operator's machine. The mechanism instead makes the claimed execution target precise
enough for a third party to replay. enough for a third party to replay.
\subsection{Consumer goals} \subsection{Consumer goals}
@ -407,7 +414,7 @@ a later view only if it is the same view or a verified extension. Two valid
heads of equal size and unequal roots, in one log context, are transferable heads of equal size and unequal roots, in one log context, are transferable
evidence that the key holder signed incompatible views. Unequal-size forks evidence that the key holder signed incompatible views. Unequal-size forks
require retained history, gossip, or a witness. The transition discipline require retained history, gossip, or a witness. The transition discipline
itself is syntactic, enforced by the pin rule by construction; the semantic itself is syntactic, enforced by the pin rule (\S4.3) by construction; the semantic
content --- an opened position cannot change value across accepted views --- content --- an opened position cannot change value across accepted views ---
is a theorem (\S\ref{sec:games}). is a theorem (\S\ref{sec:games}).
\item[G3: Policy separation.] The operator's positive label cannot make a \item[G3: Policy separation.] The operator's positive label cannot make a
@ -459,15 +466,17 @@ consistency proofs are the RFC~9162 algorithms~\cite{ct2}.
A tree head contains schema-version and type tags, a log identifier, tree A tree head contains schema-version and type tags, a log identifier, tree
size, root hash, timestamp, and hash-algorithm identifier. The canonical JSON serialization of size, root hash, timestamp, and hash-algorithm identifier. The canonical JSON serialization of
those fields is signed with Ed25519. The log identifier and version tag prevent those fields is signed with Ed25519. The log identifier and version tag prevent
cross-log and cross-protocol replay. cross-log and cross-protocol replay. We call the leaf history a head
commits to a \emph{view}, and write \emph{signed view} for that history
as represented by its signed head.
Since tree size 14, every head additionally carries a \emph{deterministic} Since tree size 14, every head additionally carries a \emph{deterministic}
SLH-DSA-SHA2-128s (FIPS~205) signature over the same payload. The SLH-DSA-SHA2-128s (FIPS~205) signature over the same payload. The
co-signature is additive: the Ed25519 signature remains the one every co-signature is additive: the Ed25519 signature remains the one every
consumer must verify, and heads published before size 14 carry no consumer must verify, and heads published before size 14 carry no
post-quantum signature --- the standalone verifier reports them as absent post-quantum signature --- the standalone verifier reports the co-signature as
rather than failing them, because an append-only log keeps the history of absent on such heads rather than rejecting them: an append-only log
its own signature scheme. Determinism is chosen as an audit primitive: a necessarily preserves the history of its own signature-scheme upgrades. Determinism is chosen as an audit primitive: a
deterministic re-sign of the same payload is byte-comparable, so ``same deterministic re-sign of the same payload is byte-comparable, so ``same
input, same signature'' becomes a diff rather than an assurance. The input, same signature'' becomes a diff rather than an assurance. The
co-signature closes a further loop: its parameter set is exactly the one co-signature closes a further loop: its parameter set is exactly the one
@ -491,6 +500,9 @@ same-size fork evidence;
\item larger size: accept iff a consistency proof verifies, then update; \item larger size: accept iff a consistency proof verifies, then update;
\item smaller size: reject as rollback. \item smaller size: reject as rollback.
\end{itemize} \end{itemize}
We call this transition discipline the \emph{pin rule}, and the persisted
pair $(n_{\mathrm{pin}},r_{\mathrm{pin}})$ the \emph{pin-store}.
Freshness is an external availability policy. A persisted pin detects rollback Freshness is an external availability policy. A persisted pin detects rollback
relative to local history; it does not prove that a client sees the globally relative to local history; it does not prove that a client sees the globally
latest signed head. latest signed head.
@ -523,9 +535,10 @@ This section states the consumer-facing arguments in the form used by the Lean
mechanization. The proofs are elementary but explicit: successful false mechanization. The proofs are elementary but explicit: successful false
openings yield concrete SHA-256 collisions rather than appealing to an informal openings yield concrete SHA-256 collisions rather than appealing to an informal
``Merkle trees are secure'' statement. The explicitness is load-bearing: over a ``Merkle trees are secure'' statement. The explicitness is load-bearing: over a
fixed-width hash a bare ``some collision exists'' is vacuously true by fixed-width hash, ``some collision exists'' is trivially true by counting;
counting, so each soundness statement is about a named extractor function, and each soundness statement therefore names an explicit extractor function,
the corpus pins a machine-checked non-vacuity guard for every extractor. and the corpus pins a machine-checked guard that each extractor's output
really is a collision (distinct preimages, equal digests).
\subsection{Inclusion} \subsection{Inclusion}
@ -588,7 +601,9 @@ $|D_0|=n_0\le n_1=|D_1|$, $D_0\neq D_1[0{:}n_0]$, and
\ConsRec(n_0,n_1,C,\top,\MTH(D_0)) \ConsRec(n_0,n_1,C,\top,\MTH(D_0))
=(\MTH(D_0),\MTH(D_1)), =(\MTH(D_0),\MTH(D_1)),
\] \]
$\mathcal{E}_{\rm cons}(D_0,D_1,C)$ returns a SHA-256 collision. $\mathcal{E}_{\rm cons}(D_0,D_1,C)$ returns a SHA-256 collision. (The hypothesis supplies the honest
$\MTH(D_0)$ as the pinned value; \S5.3 measures the deployed flow, which
has no such mechanized supplier.)
\end{theorem} \end{theorem}
\begin{proof} \begin{proof}
The new-root component is a hash fold over the shape of the $n_1$ tree. Compare The new-root component is a hash fold over the shape of the $n_1$ tree. Compare
@ -602,13 +617,16 @@ collision.
\end{proof} \end{proof}
The theorem's hypothesis pins the honest old root $\MTH(D_0)$. The deployed The theorem's hypothesis pins the honest old root $\MTH(D_0)$. The deployed
flow has no mechanized supplier of that pin; the next subsection measures what flow contains nothing mechanized that guarantees the pinned value is the
the iterative verifier does when size claims alone steer its walk. honest old root; the next subsection measures the iterative verifier's
behavior when only the claimed sizes constrain its reconstruction.
\begin{proposition}[Pin-store safety] \begin{proposition}[Pin-store safety]
Assume EUF-CMA security of the head signature and collision resistance of Assume EUF-CMA security of the head signature and collision resistance of
SHA-256. A consumer following the pin transition accepts only a nondecreasing SHA-256. A consumer following the pin transition accepts only a nondecreasing
sequence of sizes whose exhibited leaf lists are prefix-related. Two accepted sequence of sizes; if leaf lists are exhibited for two accepted heads,
they are prefix-related except under collision (see the mapping paragraph
of \S\ref{sec:games}). Two accepted
heads under the same key, in one log context, with equal size and unequal heads under the same key, in one log context, with equal size and unequal
roots are transferable evidence that the key holder signed incompatible roots are transferable evidence that the key holder signed incompatible
views. views.
@ -616,7 +634,8 @@ views.
\begin{proof} \begin{proof}
Rollback is rejected syntactically. At equal size the transition is accepted Rollback is rejected syntactically. At equal size the transition is accepted
only with equal roots; if the two exhibited equal-length leaf lists differed, only with equal roots; if the two exhibited equal-length leaf lists differed,
whole-tree binding would extract a SHA-256 collision, so under collision whole-tree root binding (each root determines its committed leaf list up
to collision) would extract a SHA-256 collision, so under collision
resistance the lists are equal. A larger head is accepted only after a resistance the lists are equal. A larger head is accepted only after a
consistency proof, so non-prefix acceptance yields a collision by the previous consistency proof, so non-prefix acceptance yields a collision by the previous
theorem. Equal-size unequal roots in one log context, with valid signatures, are two theorem. Equal-size unequal roots in one log context, with valid signatures, are two
@ -630,7 +649,7 @@ certificate is a function only of $\Obs_a(c)$ and $\Policy(c)$. An operator
label cannot change a nonconforming observation into a conforming one. label cannot change a nonconforming observation into a conforming one.
\end{proposition} \end{proposition}
\begin{proof} \begin{proof}
The comparison is set equality and takes no positive operator verdict as input. The comparison is set equality and takes no positive operator label as input.
A deployment may conservatively treat an operator failure label as a veto, but A deployment may conservatively treat an operator failure label as a veto, but
a veto cannot grant acceptance. a veto cannot grant acceptance.
\end{proof} \end{proof}
@ -989,7 +1008,7 @@ queried to the signing oracle; its valid signature is an existential forgery,
which $\mathcal{B}_{\rm fr}$ outputs. which $\mathcal{B}_{\rm fr}$ outputs.
\end{proof} \end{proof}
\begin{lemma}[Policy separation]\label{lem:policy} \begin{lemma}[Policy separation --- Proposition~2 restated for the scheme package]\label{lem:policy}
For every leaf $a$ and certificate $c$, the verdict computed by For every leaf $a$ and certificate $c$, the verdict computed by
$\mathsf{Verdict}$ equals $[\Obs_a(c)=\Policy(c)]$; it reads no operator $\mathsf{Verdict}$ equals $[\Obs_a(c)=\Policy(c)]$; it reads no operator
label, and acceptance consults the operator's status only as a veto. This is label, and acceptance consults the operator's status only as a veto. This is
@ -1008,8 +1027,8 @@ separation.
\end{definition} \end{definition}
\begin{theorem}[Collision-extractable accountability of the construction]\label{thm:main} \begin{theorem}[Collision-extractable accountability of the construction]\label{thm:main}
The LTL construction --- the RFC~9162 tree, the canonical signed heads of The LTL construction with the recursive verifiers of \S\ref{sec:security}
\S4.2 in their fixed context $\chi$, the pin rule of \S4.3, and the policy --- the RFC~9162 tree, the canonical signed heads of \S4.2 in their fixed context $\chi$, the pin rule of \S4.3, and the policy
verdict of \S\ref{sec:model} --- is collision-extractably accountable, with verdict of \S\ref{sec:model} --- is collision-extractably accountable, with
$\mathcal{B}_{\rm pb}$ ($\le 2(\lceil\log_2 n\rceil{+}1)$ hash evaluations), $\mathcal{B}_{\rm pb}$ ($\le 2(\lceil\log_2 n\rceil{+}1)$ hash evaluations),
$\mathcal{B}_{\rm hist}$ ($O(k\log n_k)$), and the one-forgery reductions $\mathcal{B}_{\rm hist}$ ($O(k\log n_k)$), and the one-forgery reductions
@ -1088,52 +1107,58 @@ per fork --- the log records both generations as separate leaves), covering:
mathematical point equation. mathematical point equation.
\end{itemize} \end{itemize}
The signature apex can be summarized as follows. Let $k$ be the challenge The signature apex is organized as four tiers T1--T4
scalar produced by an opaque SHA-512 boundary and let $r_1$ be the raw $R$ bytes (Appendix~\ref{app:tiers}). Let $c$ be the challenge scalar produced by an opaque SHA-512 boundary and let $\bar R$ be the raw $R$ bytes
from the signature. The corpus separates: from the signature. The corpus separates:
\begin{description}[leftmargin=1.5em,itemsep=2pt] \begin{description}[leftmargin=1.5em,itemsep=2pt]
\item[T1:] acceptance iff the verifier's recomputed compressed bytes equal \item[T1:] acceptance iff the verifier's recomputed compressed bytes equal
$r_1$; $\bar R$;
\item[T2:] those recomputed bytes are the canonical encoding of \item[T2:] those recomputed bytes are the canonical encoding of
$[k](-A)+[s]B$; $[c](-A)+[s]B$;
\item[T3:] canonical encoding is injective on valid curve points; \item[T3:] canonical encoding is injective on valid curve points;
\item[T4:] acceptance iff constructive decompression of $R$ yields \item[T4:] acceptance iff constructive decompression of $R$ yields
$[k](-A)+[s]B$. $[c](-A)+[s]B$.
\end{description} \end{description}
The separation keeps residual assumptions visible. SHA-512 and selected The separation keeps residual assumptions visible. SHA-512 and selected
wire-format interfaces are opaque boundaries at the apex; lower arithmetic and wire-format interfaces are opaque boundaries at the apex; lower arithmetic and
group certificates use the foundational Lean axioms observed in the corpus. group certificates use the foundational Lean axioms observed in the corpus.
\subsection{The SLH-DSA verify path: the method on second terrain}\label{sec:slhdsa} \subsection{A second instantiation: the SLH-DSA verify path}\label{sec:slhdsa}
The second campaign extracts the verification path of SLH-DSA (FIPS~205, The second campaign extracts the verification path of SLH-DSA
(FIPS~205~\cite{fips205},
parameter set SHA2-128s) from a pinned pure-Rust implementation through the parameter set SHA2-128s) from a pinned pure-Rust implementation through the
same Charon/Aeneas route, starting from one monomorphic entry point with the same Charon/Aeneas route, starting from one monomorphic entry point with the
five hash primitives marked opaque at the extraction boundary. The corpus is five hash primitives marked opaque at the extraction boundary. The corpus is
eleven certificates: ten loop-fidelity theorems (chain walking, WOTS eleven certificates: ten \emph{loop-fidelity} theorems --- each stating
recomputation and checksum, XMSS and FORS Merkle ascent, hypertree layering, that an extracted loop computes the same value as a reference recursive
digit/byte plumbing) and an acceptance characterization, fold --- covering chain walking, WOTS recomputation and checksum, XMSS and
FORS Merkle ascent, hypertree layering, and digit/byte plumbing
(Appendix~\ref{app:slhtiers} lists each with its exact cone) and an acceptance characterization,
\code{slh_verify_128s_accepts_iff}: for every message digest, signature, and \code{slh_verify_128s_accepts_iff}: for every message digest, signature, and
public key at these parameters, the extracted verifier accepts exactly when public key at these parameters, the extracted verifier accepts exactly when
the recomputed hypertree root byte-equals the public key's root --- no other the recomputed hypertree root byte-equals the public key's root --- no other
acceptance path exists. acceptance path exists.
The terrain differs from Ed25519 in one structural way, and the leaf says so. The terrain differs from Ed25519 in one structural way, and the leaf says so.
The Ed25519 bridges land in an independent second semantics For Ed25519, each theorem relates extracted code to an independent
($\mathbb{Z}/p\mathbb{Z}$, which the proof library understands without ever mathematical semantics (arithmetic over $\mathbb{Z}/p\mathbb{Z}$,
seeing the extracted code); SLH-DSA verification is hash chains and Merkle formalized with no reference to the extracted code); SLH-DSA verification
nodes all the way down, so the reference folds are built from the same five is hash chains and Merkle nodes all the way down, so its reference
uninterpreted hash oracles (\code{h_msg}, \code{f}, \code{h}, specifications are folds over the same five uninterpreted hash oracles
\code{t_l}, \code{t_len}, modeling the SHA-256 instantiations) that the (\code{h_msg}, \code{f}, \code{h}, \code{t_l}, \code{t_len}, modeling
extracted loops call. Each loop certificate therefore makes the extracted the SHA-256 instantiations --- uninterpreted function symbols in the
logic, not random oracles) that the extracted loops call --- there is no
independent second semantics to land in. Each loop certificate therefore makes the extracted
control flow \emph{visible} --- small, sequential, checkable against the control flow \emph{visible} --- small, sequential, checkable against the
standard's algorithms --- while the reading of fold against FIPS~205 remains standard's algorithms --- while the reading of fold against FIPS~205 remains
a declared human step. The audit enforces every certificate's axiom set a declared human step. The audit enforces every certificate's axiom set
exactly in both directions, and the cone \emph{grows} up the pyramid --- exactly in both directions, and the cone \emph{grows} up the pyramid ---
pure bit arithmetic rests on the kernel alone; the apex carries all five pure bit arithmetic rests on the kernel alone; the apex carries all five
oracles (Appendix~\ref{app:slhtiers}). Scope, stated in the leaf: the proved oracles (Appendix~\ref{app:slhtiers}). Scope, stated in the leaf: the proved
subject is a monomorphic facade whose bridge to the deployed generic verifier subject is a monomorphic facade (the fixed-parameter entry point above)
whose bridge to the deployed generic verifier
is a 137-case differential test; one inner digit-extraction loop carries no is a 137-case differential test; one inner digit-extraction loop carries no
certificate; signing and key generation were never extracted. certificate; signing and key generation were never extracted.
@ -1181,13 +1206,15 @@ Every signed head issued since public mirroring began is retained --- twelve
heads, at tree sizes 8 through 19, dual-signed from size 14 on --- together heads, at tree sizes 8 through 19, dual-signed from size 14 on --- together
with every leaf and receipt, in an append-only Git mirror; a clone with every leaf and receipt, in an append-only Git mirror; a clone
re-verifies the entire log offline with the repository's standalone verifier. re-verifies the entire log offline with the repository's standalone verifier.
The first twelve leaves are three four-fork replay generations. Leaves 0--3 The first twelve leaves are three replay generations across the four
Ed25519 codebases. Leaves 0--3
record a failed audit run and remain permanently visible. Leaves 4--7 record a record a failed audit run and remain permanently visible. Leaves 4--7 record a
clean replay. Leaves 8--11 re-attest rewritten repository histories rather clean replay. Leaves 8--11 re-attest rewritten repository histories rather
than replacing the old leaves. Leaf 12 attests the accumulator's own Lean than replacing the old leaves. Leaf 12 attests the accumulator's own Lean
corpus (\S\ref{sec:deployment}, E3); leaves 13--16 re-attest the four corpus (\S\ref{sec:deployment}, E3); leaves 13--16 re-attest the four
Ed25519 corpora at 44 certificates each; leaf 17 re-attests the accumulator Ed25519 corpora at 44 certificates each; leaf 17 re-attests the accumulator
corpus at its hardened state; and leaf 18 attests the SLH-DSA-SHA2-128s corpus at its hardened state (the same corpus after closure of external
review findings); and leaf 18 attests the SLH-DSA-SHA2-128s
verification path --- the log's first post-quantum subject, and the scheme verification path --- the log's first post-quantum subject, and the scheme
that has co-signed every head since size 14. A leaf whose pinned commit ceases to be that has co-signed every head since size 14. A leaf whose pinned commit ceases to be
distributed decays from a replayable claim to a historical record; consumers distributed decays from a replayable claim to a historical record; consumers
@ -1252,7 +1279,8 @@ path. Heads are dual-signed from size 14 on.}
Leaf 12 is not a claim that the whole service is formally verified. The Lean Leaf 12 is not a claim that the whole service is formally verified. The Lean
corpus covers the recursive Merkle model, inclusion completeness and corpus covers the recursive Merkle model, inclusion completeness and
collision-extracting soundness, the consistency extractor, and the Merkle-layer collision-extracting soundness, the consistency extractor, and the Merkle-layer
share of pin-store safety. The abstract root-binding lemma from the paper is share of pin-store safety. The folklore whole-tree root-binding property (a root determines its
committed leaf list up to SHA-256 collision) is
mechanized through the specializations needed by the extractors rather than as mechanized through the specializations needed by the extractors rather than as
one quantified hash-fold theorem. Signature unforgeability, execution one quantified hash-fold theorem. Signature unforgeability, execution
provenance, the full signed-head state machine, asymptotic cost, and the provenance, the full signed-head state machine, asymptotic cost, and the
@ -1278,9 +1306,10 @@ Scheme-level games (\S\ref{sec:games}) & paper-level explicit reductions & two-t
\subsection{Cost and reproducibility} \subsection{Cost and reproducibility}
A replay of one Ed25519 fork requires approximately 30 minutes of end-to-end A replay of one Ed25519 fork requires approximately 30 minutes of end-to-end
guarded replay time under the pinned environment, a figure corroborated by the resource-guarded (memory- and time-capped) replay time under the pinned environment, a figure corroborated by the
inter-leaf issuance spacing visible in the published log. Receipt verification requires one Ed25519 inter-leaf issuance spacing visible in the published log. Receipt verification requires one Ed25519
signature and a logarithmic number of SHA-256 node computations. The signature and a logarithmic number of SHA-256 node computations (the
complete inclusion core is printed as Appendix~\ref{app:verifier}). The
accumulator corpus is independently reviewable with a pinned public Lean accumulator corpus is independently reviewable with a pinned public Lean
release; an environment-derived inventory fails closed on added, removed, or release; an environment-derived inventory fails closed on added, removed, or
axiom-smuggling declarations. axiom-smuggling declarations.
@ -1381,8 +1410,9 @@ explicitly open.
\section{Limitations and research agenda}\label{sec:limitations} \section{Limitations and research agenda}\label{sec:limitations}
The subject corpus maintains a numbered ledger of fifteen known gaps together The subject corpus maintains a numbered public file, \code{KNOWN-GAPS},
with their closure options; this section groups the load-bearing ones. of fifteen gaps with their closure options (the scope block of
Appendix~\ref{app:entry13} cites its items 14 and 15); this section groups the load-bearing ones.
\paragraph{Operator observation trust.} \paragraph{Operator observation trust.}
A malicious operator can fabricate a replay report. Signatures and Merkle A malicious operator can fabricate a replay report. Signatures and Merkle
@ -1416,7 +1446,7 @@ isolated clients to receive that view. Independent witnesses or gossip are the
natural next deployment step. natural next deployment step.
\paragraph{Consistency refinement.} \paragraph{Consistency refinement.}
The recursive model is proved; the iterative deployment diverges from it on The recursive model is proved; the iterative deployment diverged from it on
malformed inputs, every observed divergence being deployed-accepts-only. The strongest closure is either to deploy malformed inputs, every observed divergence being deployed-accepts-only. The strongest closure is either to deploy
$\ConsRec$-equivalent semantics or to mechanize the signed-head and pin-store $\ConsRec$-equivalent semantics or to mechanize the signed-head and pin-store
flow and prove the authentic-pair refinement theorem. flow and prove the authentic-pair refinement theorem.
@ -1486,7 +1516,7 @@ The author designed the system and is responsible for every claim. Claude
tooling, and manuscript review. Their output was not accepted as evidence; tooling, and manuscript review. Their output was not accepted as evidence;
claims were retained only after human review or reproducible artifact checks. claims were retained only after human review or reproducible artifact checks.
\begin{thebibliography}{22} \begin{thebibliography}{23}
\itemsep2pt \itemsep2pt
\bibitem{ct1} B. Laurie, A. Langley, E. K\"asper. Certificate Transparency. \bibitem{ct1} B. Laurie, A. Langley, E. K\"asper. Certificate Transparency.
RFC 6962, 2013. RFC 6962, 2013.
@ -1566,6 +1596,9 @@ Collision-Resistant Hashing without the Keys. VIETCRYPT, LNCS 4341, pp.
Verification Pipeline with AI Provers: An Experience Report. arXiv:2605.30106, Verification Pipeline with AI Provers: An Experience Report. arXiv:2605.30106,
2026. 2026.
\bibitem{fips205} National Institute of Standards and Technology.
Stateless Hash-Based Digital Signature Standard. FIPS 205, August 2024.
\end{thebibliography} \end{thebibliography}
% Appendix policy (declared 2026-08-16): the appendix block starts on a % Appendix policy (declared 2026-08-16): the appendix block starts on a
@ -1682,6 +1715,11 @@ T4 & constructive decompression lift & \code{verify_accepts_iff_decompress} \\
\end{tabular} \end{tabular}
\end{center} \end{center}
All four tiers share one opaque boundary --- the SHA-512 challenge hash
and the selected wire-format interfaces (\S\ref{sec:instantiation});
the arithmetic and group certificates beneath them rest on Lean's
foundational axioms alone.
\section{SLH-DSA verification certificates and their cones}\label{app:slhtiers} \section{SLH-DSA verification certificates and their cones}\label{app:slhtiers}
Eleven certificates over the extracted SLH-DSA-SHA2-128s verify path Eleven certificates over the extracted SLH-DSA-SHA2-128s verify path
@ -1715,10 +1753,10 @@ The oracles model the parameter set's SHA-256 hash-suite instantiations:
\code{h} (Merkle node), \code{t_l} and \code{t_len} (the WOTS and FORS \code{h} (Merkle node), \code{t_l} and \code{t_len} (the WOTS and FORS
compressors --- two axioms over what is one Rust primitive, deliberately compressors --- two axioms over what is one Rust primitive, deliberately
conservative, with the source's naming inversion against the standard's conservative, with the source's naming inversion against the standard's
$T_\ell$/$T_k$ documented at the declarations). The acceptance $T_\ell$/$T_k$ documented at the declarations). The acceptance characterization is proved directly from the verifier's
characterization is a structural factorization, not a composition of the structure, not by composing the ten loop theorems --- it would remain
loop theorems: it would remain provable if any of the ten were deleted, provable if any of the ten were deleted. Conversely, each loop
and each loop certificate is meaningful exactly to the extent its certificate carries assurance only insofar as a human has checked its
reference fold has been read against FIPS~205. reference fold against the corresponding FIPS~205 algorithm.
\end{document} \end{document}

2
provider/src/pacta_provider/webdocs.py
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@ -392,7 +392,7 @@ our roadmap.</strong> (The full walk-through is lecture&nbsp;11 of the Jupyter c
<h2>The paper</h2> <h2>The paper</h2>
<div class="card"><a href="{base}/paper"><strong>Accountable Distribution of Machine-Checked <div class="card"><a href="{base}/paper"><strong>Accountable Distribution of Machine-Checked
Correctness Evidence: A Transparency Model and the Lean Transparency Log</strong></a> Correctness Evidence: A Transparency Model and the Lean Transparency Log</strong></a>
(PDF, 25 pages, <strong>v0.12 — revised August&nbsp;2026</strong>; the version is printed on the (PDF, 25 pages, <strong>v0.13 — revised August&nbsp;2026</strong>; the version is printed on the
title page) — the trust decomposition (expensive verification produces an title page) — the trust decomposition (expensive verification produces an
observation; transparency makes the observation accountable; consumer-local policy decides observation; transparency makes the observation accountable; consumer-local policy decides
acceptance), collision-extracting soundness for inclusion and consistency, scheme-level acceptance), collision-extracting soundness for inclusion and consistency, scheme-level